One hundred years after Einstein predicted the existence of gravitational waves on the basis of his theory of General Relativity, LIGO announced the first observation of gravitational waves passing through the Earth emitted by the collision of two black holes one billion three-hundred million light years away. The detection of gravitational waves constitutes a major scientific discovery, as it permits a new kind of observation of the cosmos, quite different from electromagnetic and particle observations. In this talk I will review the theoretical groundwork that allowed to identify and interpret the gravitational-wave signals, and discuss how those new astronomical messengers can unveil the properties of the most extreme astrophysical objects in the universe, and inform us about the theory of gravity in the highly dynamical space-time regime.